Expressions and equations
determine if each of the following expressions is equ
each of the following expressions is equivalent to 24 - 6x. explain your
reasoning for each.

a. Yes

b. Yes

c. Yes

d. No

Step-by-step explanation:

a. Because -10x+4x=6x

b. 2(12-3x)=2*12-2*3x=24-6x

c. 24 and -6x just switched places.

d. 24x-6x=18x not 24-6x

the answer is d

step-by-step explanation:

y+3=-4(x-2)

y+3=-4x+8

  -3         -3  

y=-4x+5

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4